Digital subscriber lines (DSLs) are technologies designed to provide access to electronic data by communicating over wires of traditional local telephone networks. Example DSL technologies include asymmetric digital subscriber line (ADSL) and very high speed digital subscriber line (VDSL), which are methods of communicating data over twisted pairs (also known as copper pairs, subscriber loop, or plainly loop). At their inception, twisted pairs were designed and deployed to support relatively low bit rates and low data content suitable for voice signals, and were not designed to carry high bit rates, especially in today's ever-growing need for high speed broadband Internet access. To supply the demand for high speed communications, optical fibers are increasingly being deployed and employed owing to their inherent greater data-carrying capacities and excellent immunity to crosstalk in comparison to those of copper pairs. The deployment of optical fiber in the last few hundred meters to the customer's terminal equipment, however, accounts for the greater part of the overall cost, the result of which compels communication operators to strive to deploy optical fiber increasingly closer to the end-user to increase performance, while concurrently bridging the troublesome remaining distance by using the existing infrastructure of twisted pairs. A disadvantage of using the existing copper wire infrastructure over “last-mile” telecommunications to the end-user is the fact that multiple copper wires stranded in parallel within a cable binder generate undesired electromagnetic interference on each other when signals are transmitted therethrough, what is known as crosstalk. Essentially, there are two kinds of crosstalk, near-end crosstalk (NEXT) and far-end crosstalk (FEXT). Known techniques to reduce NEXT may involve, for example, the use of frequency division multiplexing (FDM). FEXT is known to adversely affect performance (e.g., data bit rates) in the communication of data over VSDL implemented hardware, which utilizes relatively high frequencies and bandwidth (e.g., up to 30 MHz of bandwidth).
Techniques for crosstalk cancellation that employ the precoding of data prior to its transmission are known in the art as “vectoring”. Vectoring technology is used today to enhance the performance of VDSL transceivers. By the use of vectoring methods, FEXT noise is substantially cancelled, which results in higher signal to noise ratios (SNRs) as well as higher bit-rates. Known vectored VDSL solutions, take advantage of the fact that the FEXT intensity level, though significant, is still much lower in comparison to the signal strength level. In a formal mathematical representation of communication channels that couple between transmitters and receivers, the channels' responses for a given frequency are represented by a matrix. The main diagonal of the channel matrix relates to the direct channels, whereas the off-diagonal elements in the channel matrix represent the cross-talk channels.
Two basic precoding schemes known in the art are linear precoding and non-linear precoding. An article entitled “A Near-Optimal Linear Crosstalk Precoder for Downstream VDSL”, by R. Cendrillon et al., published by the journal entitled “IEEE Transactions on Communications”, Vol. 55, No. 5, on May 2007 is directed to linear precoding via a linear crosstalk precoder for VSDL. This article describes the crosstalk precoder for downstream VSDL having a relatively low run-time complexity. This crosstalk precoder is based on a channel diagonalizing criterion, which requires transmitter-side operations only, and thus possesses a relatively lower complexity than the (non-linear) Tomlinson-Harashima precoder (THP), as it does not require additional receiver-side operations. Thus, the precoder presented in the article is denoted as a “diagonalizing precoder” (DP). The article claims that due to the row-wise diagonal dominance (RWDD) of the downstream VSDL channel, the DP achieves near-optimal performance.
An article entitled “A Multi-user Precoding Scheme achieving Crosstalk Cancellation with Application to DSL systems” by G. Ginis and J. M. Cioffi, published in the Thirty-Fourth Asilomar Conference on Signals, Systems and Computers, held on Oct. 29, 2000-Nov. 1, 2000, describes a non-linear precoding scheme capable of achieving crosstalk cancellation involving communication between a base station and a plurality of geographically dispersed users. The non-linear precoding scheme described, borrows from the principles of the THP that is used for equalization against inter-symbol interference (ISI) and has application to DSL systems. The non-linear precoding scheme employs an equalization structure that achieves zero-forcing (ZF) equalization of a MIMO channel. Further described is the use of the non-linear precoding scheme in combination with multi-carrier modulation (e.g., discrete multi-tone (DMT)), for channels with memory, which as has application to DSL systems.